I really have to disagree that the significant figure approach doesn't make
any sense. To be sure there are better (and more complex) approaches, but
when I cover this--and it takes 15 minutes of class time--the primary
example given is finding an area from two measurement one with a micrometer
(4 sig figs) and the other with a plastic ruler (2 sig figs). Assuming
(and yes this is the sore point) that the uncertainty is 1 in the last
digit, it is easy to show that the 'rule' of keeping 2 sig figs in the
product does make sense versus keeping 4 or more. Armed with this short
example and a hand-out of the 'rules', we can do simple but reasonable labs.
I would also be against the three-decimal place rule you suggest. For
example, we do some simple Ohm's law labs using VI graphs to get the
resistances of some 'black boxes', individually and in series and parallel.
The digital voltmeter reads to a 100th of a volt and we use a 0-10 volt
range and the analog ammeters can be read to no better than 3 digits. Now
we go to EXCEL for graphing and fitting. Typically the resistances are in
the 50-200 ohm range. I really don't see that letting students report that
the resistance was 125.264 Volts/Amp is reasonable. I really want 125 or at
worst 125.3 as the reported value. Sig Figs handles this.
In another lab (first lab of the year) we measure densities to identify the
material of objects, some quite regular but others of no simple geometrical
shape. Some of the samples can be measured quite accurately and the
expected uncertainty in the student's densities can be on the order of .5%
or less. However, we have irregularly shaped objects that are cast aluminum
(don't look like aluminum) and are measured using water displacement. Here
there is a much larger uncertainty because of the precision that students
can read their graduated beakers. Reasonable uncertainties in the densities
can be as high as 5%. Again sig figs takes care of this.
I guess the fact that some of us went through college with slide rules is
the reason we never really encountered these questions until hitting real
research at the graduate level (my work measuring nuclear masses using
accelerated particles and a very large magnetic spectrograph quickly
introduced me to all the complexities!)
I do use sig figs at the intro level with the caveat that this is a 'crude'
(but I believe meaningful in most cases) technique that will need to be
refined (replaced later). I clearly point out that if the uncertainty in a
ruler measurement is +/- 0.5 mm, our technique will underestimate
uncertainties in our calculated values. Like John M, after the first couple
labs, I do not get too upset (i.e. take off points) for one too many or one
too few sig figs, but stay vigilant for students not recording their data to
the proper precision available with their instruments.
I'll leave it at this since historically I know we will not reach a
universal agreement here--(what makes sense to one person seems not to make
sense to another)--hence the constantly reoccurring thread! ;-)
Rick
Richard W, Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
Free Physics Educational Software at:
www.saintmarys.edu/~rtarara/software.html
Most software updated in 2011
-----Original Message-----
From: John Denker
As for artists and poets, do the experiment sometime. I have.
When I ask a practicing artist if they learned about sig figs
in high school, they usually say something like "Yeah, I
remember something about that, but it never made any sense
to me."
To which I reply: "There's a reason why it never made any
sense to you. That's because it doesn't make any sense."
1) As I have said before, if the class is not ready for any real
appreciation of uncertainty, don't teach them sig figs. Just
tell them to round everything off to 3 decimal places (in
scientific notation) and leave it at that. (Worrying about
the uncertainty can come later, if at all.)
Surely there are already not enough hours in your day, and not
enough minutes in each hour of class. Surely the time spent
on sig figs could be better spent on something that actually
makes sense ... something that will not have to be unlearned
later.